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Re: Weiner process

  • To: mathgroup at smc.vnet.net
  • Subject: [mg63909] Re: Weiner process
  • From: "Valeri Astanoff" <astanoff at yahoo.fr>
  • Date: Sat, 21 Jan 2006 04:58:47 -0500 (EST)
  • References: <dqqc98$m0j$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Don wrote:
> For a Monte Carlo simulation I need samples of the Brownian motion
> (Wiener)process X(t), 0<t<1.  Does anyone know of a data base where I can
> find them, or of a program to generate them?

This function, copied from the book
"Modelling financial derivatives with Mathematica"
by William T.Shaw, may be useful :


In[1]:= norm = Compile[{mu,sigma},
      Module[{va=1.,vb,rad=2.0,den=1.},
        While[rad >= 1.0,
          (va = 2.*Random[]-1.0;
           vb = 2.*Random[]-1.0;
           rad = va*va+vb*vb)];
        den = Sqrt[-2.0*Log[rad]/rad];
        mu+sigma*va*den]];


Example :

In[2]:=
NestList[#+norm[0,1]&,0,10]

Out[2]=
{0,-0.564281,-0.35982,-0.962551,-1.04808,-1.40842,
-3.04235,-1.51069,-0.787503,-2.0541,-2.54072}


hth

v.a.


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